# Problem with Wolfram's online integrator

• BenVitale
In summary, Wolfram's online integrator reported that it couldn't do it, but www.quickmath.com and yacas both gave the same results (as quickmath). sympy took infinite time to solve (as with most complex cases), so I concluded there was something wrong with the question itself.
BenVitale
I tried to do integral[cos(x)]^x dx

but Wolfram's online integrator reported that it couldn't do it

Am I missing something?

From your syntax it is not clear if you want to take the integral of cos(x)^x or if you want to take the integral of cos(x) and then raise that to the power of x. If it is the first then there is probably no known closed form solution for that integral.

Wolfram is not that good.

Try www.quickmath.com, it's better; or if you're on Linux, there're plenty of computer algebra systems.

However this time quickmath also failed...very hilarious answer.

$$\int \sp{\displaystyle x} {{{\cos \left( { \%M} \right)} \sp \%M} \ {d \%M}}$$

yacas gives the same results (as quickmath).

sympy takes infinite time to solve (as with most complex cases)

So I conclude there's something wrong with the question itself.

DaleSpam said:
From your syntax it is not clear if you want to take the integral of cos(x)^x or if you want to take the integral of cos(x) and then raise that to the power of x.
.

It's taking the integral of cos(x)^x

dE_logics said:
So I conclude there's something wrong with the question itself.

Maybe, maybe not. I thought of a manipulation:

I figure that for all values of x, cos x will fall in [-1,+1].
So, taking the integral of cos(x)^x is equivalent to taking the integral of x^x over [-1,0] and [0,+1]

What do you think?

By that logic the integral would be the same as sin(x)^x or frac(x)^x or saw(x)^x or any other function bounded between -1 and 1.

DaleSpam said:
By that logic the integral would be the same as sin(x)^x or frac(x)^x or saw(x)^x or any other function bounded between -1 and 1.

Oh, yes. I see your point. I'm at loss here. What do you suggest?

I believe there is no closed form for this integral. You will have to evaluate it numerically.

## 1. What is Wolfram's online integrator?

Wolfram's online integrator is a tool provided by the popular computational knowledge engine, Wolfram Alpha. It allows users to easily calculate and solve integrals online using various methods and techniques.

## 2. What are some common issues with Wolfram's online integrator?

Some common issues with Wolfram's online integrator include incorrect or inaccurate results, difficulty handling certain types of integrals, and limitations on the number of steps or complexity of the integral that can be solved.

## 3. How can I ensure accurate results when using Wolfram's online integrator?

To ensure accurate results, it is important to carefully input the integral in the correct format and to double check the result using another method or tool. It is also helpful to have a basic understanding of integration techniques and common pitfalls.

## 4. Is there a cost to use Wolfram's online integrator?

No, Wolfram's online integrator is free to use for anyone with internet access. However, there is a paid version of Wolfram Alpha that offers additional features and capabilities.

## 5. Are there alternatives to Wolfram's online integrator?

Yes, there are many other online integrators and mathematical tools available, such as Symbolab and Mathway. It is always a good idea to compare results from different sources to ensure accuracy.

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